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With a sharp paring knife, cut the stem from each artichoke and trim the tough outer leaves to reach the inner core of soft, light green leaves.

Bring 2 gallons of water to the boil in a large, nonreactive pot. Add the artichokes, lemons, salt, and bay leaves. Cover, reduce the heat to low, and simmer until the artichokes are tender and the base can easily be pierced with the tip of a knife, about 25 minutes. Drain the artichokes in a colander and allow to cool before handling.

Remove the outer leaves of the artichokes, and with the tip of a spoon, scoop the fuzzy choke from the center of the artichoke bottoms.